Problem: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-4x-9y &= 6 \\ -5x-4y &= -7\end{align*}$
Answer: Begin by moving the $x$ -term in the second equation to the right side of the equation. $-4y = 5x-7$ Divide both sides by $-4$ to isolate $y$ $y = {-\dfrac{5}{4}x + \dfrac{7}{4}}$ Substitute this expression for $y$ in the first equation. $-4x-9({-\dfrac{5}{4}x + \dfrac{7}{4}}) = 6$ $-4x + \dfrac{45}{4}x - \dfrac{63}{4} = 6$ Simplify by combining terms, then solve for $x$ $\dfrac{29}{4}x - \dfrac{63}{4} = 6$ $\dfrac{29}{4}x = \dfrac{87}{4}$ $x = 3$ Substitute $3$ for $x$ back into the top equation. $-4( 3)-9y = 6$ $-12-9y = 6$ $-9y = 18$ $y = -2$ The solution is $\enspace x = 3, \enspace y = -2$.